Homotopy rigidity for quasitoric manifolds over a product of simplices

Abstract

We consider a variation of the Cohomological Rigidity Problem: whether two quasitoric manifolds whose cohomology rings are isomorphic are homotopy equivalent. We show that if two quasitoric manifolds have isomorphic cohomology rings and the associated polytope of one of them is a product of simplices, then they are homotopy equivalent after localizing away from an explicit list of primes.

arXiv comment16 pages